Re: Erf funcion

• To: mathgroup at smc.vnet.net
• Subject: [mg123948] Re: Erf funcion
• From: Szabolcs Horvát <szhorvat at gmail.com>
• Date: Mon, 2 Jan 2012 02:43:30 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <jdp256\$rqi\$1@smc.vnet.net>

```I'd like to link to the same question asked earlier here:

http://stackoverflow.com/questions/8523505/using-alternative-special-functions-in-simplify-and-expand

There is one (partial?) answer there.

Vicent mentioned there that he would like to get expressions in terms of
FiX, while keeping the definition FiX[x_] := ...   I believe this is not
possible (except perhaps through some formatting tricks with Defer/HoldForm)

On 2012.01.01. 8:31, Vicent wrote:
> Hello.
>
> I have an expression that depends on the Cumulative Distribution
> Function (CDF) of a Normal Variable with mean = 0 and standard
> deviation = 1.
>
> When I perform operations and/or derivatives with/for that function
> with Mathematica, I get expressions involving Erf function, as the CDF
> function of a Normal distributed variable and Erf (error function) are
> closely related. Concretely,
>
>      FiX[x] == (1/2)*(1 + Erf[x/Sqrt[2]])
>
> and thus
>
>      Erf[x] == 2*FiX[x*Sqrt[2]] - 1
>
> where FiX stands for the previously mentioned CDF, I mean:
>
>      X = NormalDistribution[0, 1]
>      FiX[x_] := CDF[X, x]
>
>
> Is there a quick way to ask Mathematica not to use  Erf  but always
> let the results as a function of FI[x]??
>
> The expressions I get as a result of my computations are larger than
> this short example:
>
>      3 (2^(7/2 - 2 (k + t))) Cp (  E^(-d^2 - (36 Cp^2)/lambda^2))
> ((Erf[(-d + (6 Cp)/lambda)/Sqrt[2]] + Erf[(6 Cp + d lambda)/(Sqrt[2]
> lambda)])^k)
>
> where "Cp", "k", "t", "d" and "lambda" are parameters or arguments
> that I want to keep as "generic".
>
> So, how can I "translate" expressions such as the last one into "FiX
> mode"? Or, better, how can I prevent Mathematica to reduce everything
> to "Erf mode"??
>
> I hope my question is clear enough... :)
>
>
> And have a good new year!
>
>

--
Szabolcs Horvát
Mma QA site proposal: http://area51.stackexchange.com/proposals/37304

```

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